Annals of Pure and Applied Logic 165 (2):620-630 (2014)

Abstract
Given a cardinal κ that is λ-supercompact for some regular cardinal λ⩾κ and assuming GCH, we show that one can force the continuum function to agree with any function F:[κ,λ]∩REG→CARD satisfying ∀α,β∈domα F. Our argument extends Woodinʼs technique of surgically modifying a generic filter to a new case: Woodinʼs key lemma applies when modifications are done on the range of j, whereas our argument uses a new key lemma to handle modifications done off of the range of j on the ghost coordinates. This work answers a question of Friedman and Honzik [5]. We also discuss several related open questions
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DOI 10.1016/j.apal.2013.09.001
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References found in this work BETA

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Tall Cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.
Easton’s Theorem and Large Cardinals.Sy-David Friedman & Radek Honzik - 2008 - Annals of Pure and Applied Logic 154 (3):191-208.

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Easton's Theorem for the Tree Property Below ℵ.Šárka Stejskalová - 2021 - Annals of Pure and Applied Logic 172 (7):102974.

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